Convergence of solutions of mixed stochastic delay differential equations with applications

Yuliya Mishura, Taras Shalaiko and Georgiy Shevchenko

Applied Mathematics and Computation, 2015, vol. 257, issue C, 487-497

Abstract: The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a γ-Hölder continuous process with γ>1/2 (e.g. a fractional Brownian motion with Hurst parameter greater than 1/2). It is shown that its solution depends continuously on the coefficients and the initial data. Two applications of this result are given: the convergence of solutions to equations with vanishing delay to the solution of equation without delay and the convergence of Euler approximations for mixed stochastic differential equations. As a side result of independent interest, the integrability of solution to mixed stochastic delay differential equations is established.

Keywords: Mixed stochastic differential equation; Stochastic delay differential equation; Convergence of solutions; Fractional Brownian motion; Vanishing delay; Euler approximation (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:487-497

DOI: 10.1016/j.amc.2015.01.019

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